"The Book of Romans was written by Paul to the believers in Rome in 58 A.D. If we take your date of Peter's death at 67 A.D., that hardly leaves enough room for him to be the bishop or hold any kind of so-called "petrine office" for "decades" at Rome. Paul mentioned in his greetings many people at Rome, but he never mentioned Peter. Surely, if Peter had been there he would have sent him greetings, just as he sent his greetings to Aquilla and Priscilla. Was he not just as important as they? The fact is that Peter was not in Rome. He may have been in Rome for his death, but even that can not be proven dogmatically. If it was the place of his death, he no doubt was hunted down by the Roman authorities and brought there as a criminal to die. There is no proof that was his place of residence, and no proof that he ever pastored a church there, much less was the Bishop. That is all a Catholic dream, a tradition with no historical basis in fact."
I will disagree with you and as proof offer these quotes from some guys you might have heard from.
Irenaeus
"Matthew also issued among the Hebrews a written Gospel in their own language, while Peter and Paul were evangelizing in Rome and laying the foundation of the Church" (Against Heresies, 3, 1:1 [A.D. 189]).
Clement of Alexandria
"The circumstances which occasioned . . . [the writing] of Mark were these: When Peter preached the Word publicly at Rome and declared the gospel by the Spirit, many who were present requested that Mark, who had been a long time his follower and who remembered his sayings, should write down what had been proclaimed" (Sketches [A.D. 200], in a fragment from Eusebius, History of the Church, 6, 14:1).
Tertullian
"But if you are near Italy, you have Rome, where authority is at hand for us too. What a happy church that is, on which the apostles poured out their whole doctrine with their blood; where Peter had a passion like that of the Lord, where Paul was crowned with the death of John [the Baptist, by being beheaded]" (Demurrer Against the Heretics 36 [A.D. 200]).
Eusebius of Caesarea
"[In the second] year of the two hundredth and fifth Olympiad [A.D. 42]: The apostle Peter, after he has established the church in Antioch, is sent to Rome, where he remains as a bishop of that city, preaching the gospel for twenty-five years" (The Chronicle [A.D. 303]).
Lactantius
"When Nero was already reigning, Peter came to Rome, where, in virtue of the performance of certain miracles which he worked . . . he converted many to righteousness and established a firm and steadfast temple to God. When this fact was reported to Nero . . . he sprang to the task of tearing down the heavenly temple and of destroying righteousness. It was he that first persecuted the servants of God. Peter he fixed to a cross, and Paul he slew" (The Deaths of the Persecutors 2:5 [A.D. 318]).
Optatus
"You cannot deny that you are aware that in the city of Rome the episcopal chair was given first to Peter; the chair in which Peter sat, the same who was head—that is why he is also called Cephas [‘Rock’]—of all the apostles; the one chair in which unity is maintained by all" (The Schism of the Donatists 2:2 [A.D. 367]).
Jerome
"Simon Peter, the son of John, from the village of Bethsaida in the province of Galilee, brother of Andrew the apostle, and himself chief of the apostles, after having been bishop of the church of Antioch and having preached to the Dispersion . . . pushed on to Rome in the second year of Claudius to overthrow Simon Magus, and held the sacerdotal chair there for twenty-five years until the last, that is the fourteenth, year of Nero. At his hands he received the crown of martyrdom being nailed to the cross with his head towards the ground and his feet raised on high, asserting that he was unworthy to be crucified in the same manner as his Lord" (Lives of Illustrious Men 1 [A.D. 396]).